This invention, in general, relates to interferometric methods and apparatus for measuring linear and/or angular displacements and, in particular, to apparatus and methods by which fluctuations in the index of refraction in the measurement path of a displacement measuring interferometer (DMI) can be accurately compensated for in determinations of displacement.
High-precision displacement measuring interferometry (DMI) depends on an accurate determination of the index of refraction, n, in the measurement path. One way to determine n is to place sensors in close proximity to the measurement path to monitor thermodynamic properties such as pressure, temperature, and humidity, and then use the values of those parameters together in well-known expressions relating index of refraction to monitored properties as, for example, Edlxc3xa9n""s equation with modern corrections for the index of refraction of air (See xe2x80x9cRecent advances in displacement measuring interferometryxe2x80x9d, Bobroff, Norman, Measurement Science and Technology, Vol. 4, Number 9, September 1993). If required, sensors for detecting the composition of the gas in the measurement path may also be employed to further refine the calculation of the index of refraction. For example, CO2 sensors may be usefully employed.
While few applications require greater absolute accuracy in the calculated value of n than can be obtained using Edlxc3xa9n""s equation in combination with environmental monitoring, all DMI systems are extremely sensitive to index fluctuations after initialization. This is particularly true for the case of a microlithography tool where DMI metrology is an integral part of the wafer and reticule positioning systems. Here, the most severe requirements are placed on the repeatability and stability of the DMI measurements for the purposes of accurate overlay.
In addition to providing continuous data free of high-frequency noise, a microlithography DMI must be stable over the entire time needed for a single wafer exposure, including whatever time is needed for wafer alignment. For some measurements, such as establishing the xe2x80x9cbaselinexe2x80x9d metrology between through-the-lens and off-axis alignment sensors, the interferometer system must be stable for several hours. In both of these situations, undetected changes in the index n can have serious consequences. A typical target stability for DMI in the next generation of steppers is 1 nm. The corresponding minimum allowable fluctuation in index in the measurement path is therefore 10xe2x88x929 over a 1-m distance within a bandwidth of 10xe2x88x924 to 102 Hz. Detection of these fluctuations is presently beyond the capability of environmental sensors.
Accordingly, there has been a great deal of interest in compensation systems that deal with the problem of fluctuations in the refractive index n for microlithography tools. One approach has been the use of a refractometer, also called a wavelength tracker or compensator. Such devices, which are commercially available, are actually relative refractometers. If properly positioned in the path of the forced air flow in a photolithography tool, the information from a refractometer can be used to accurately compensate for low frequency (e.g. 10xe2x88x922 Hz) changes in index.
Another approach to this problem has been the use of air turbulence compensation systems (ATC), which are based on dispersion interferometry. ATC systems use two widely-separated wavelengths and rely on the wavelength dependence of index of refraction. This wavelength dependence is characterized by the inverse dispersive power xcex93, which is the ratio of the refractivity at one wavelength to the difference in refractivity between two wavelengths. Typical values of xcex93 for air are between 15 and 75.
It is accordingly, a primary object of this invention to provide apparatus and methods by which dispersion interferometry may be combined with refractometry to compensate for both short and long term index of refraction fluctuations that may occur in the measurement path of an interferometer.
It is another object of this invention to provide apparatus and methods by which the inverse dispersion power may be initialized and monitored prior to displacement calculations.
It is yet another object of the invention to provide apparatus and methods by which index of refraction may be determined by using known physical lengths.
Other objects will in part be obvious and will in part appear hereinafter when the following detailed description is read in connection with the drawings.
The invention combines dispersion interferometry with refractometry to compensate for refractive index fluctuations over both short and long time periods. It, accordingly, includes a method and means for weighting the dispersion and refractometry data, as well as a method and means of initializing xcex93 so that the dispersion and refractometry data are self consistent and can be used to accurately calculate physical displacements.
The inventive apparatus comprises:
interferometer means employing at least two wavelengths at least a first one of which is used for measuring the displacement of an object along a measurement path and for detecting short-term fluctuations in the refractive index of air directly within the measurement path by means of the inverse dispersive power xcex93 or its equivalent;
at least one refractometer means for measuring the long-term variations in refractive index of air directly for at least the first wavelength, placed as close as practicable to the measurement path, and preferably within the path of any forced airflow directed at the measurement path;
initialization means for establishing an initial value of the inverse dispersive power xcex93 using refractometer and dispersion data acquired during a change in the length of the measurement path; and
computational means for analyzing data from the refractometer and said dispersion interferometer and for providing a calculated refractive index along said measurement path, said calculated refractive index incorporating both long- and short-term fluctuations and employing said initial value of said inverse disperse power xcex93.
In another aspect the interferometer means may be in the form of a separate displacement interferometer operating at the first wavelength and a second dispersion interferometer operating at two wavelengths, one of which may be the first wavelength.
Another aspect of the invention is a method comprising the steps of:
storing a self-consistent value of inverse dispersive power, xcex93. Initially, this may be assumed and later updated as significant changes in it occur;
measuring the refractive index for xcex1 using a refractometer located near the measurement path;
determining a time average for the refractive index generated in step over a characteristic time period (Eq. 3)
measuring the optical path length of the measurement path for wavelengths, xcex1,2 (Eq. 2);
calculating the local index, N12xcex using dispersion interferometry (Eq. 6);
time averaging the local dispersion (Similar to Eq. 3);
calculating the fluctuation the local index as the difference between the instantaneous value and time averaged value (Eq. 4);
calculating the physical distance corrected for atmospheric effects (Eq. 6; and
testing for the difference between the time averaged value of the local index and the time averaged value of the index at the refractometer;
calibrating xcex93 and updating its value should xcex93 change significantly.
Another aspect of the invention relates to a method for calibrating the inverse dispersive power comprising the steps of:
measuring the refractive index for xcex1 using a refractometer near the measurement path;
determining the time average of the refractive index near the measurement path over a characteristic time T;
moving the stage between two positions;
measuring the change in optical path length of the measurement path for two wavelengths, xcex1,2;
calculating the inverse dispersive power, xcex93, using Eq. 1; and
returning to the measurement path with the value for xcex93.
In yet another aspect of the invention, the index is determined by using a known physical distance between two reference points instead of a refractometer.